外文翻譯--進(jìn)料溫度和質(zhì)量流量的變化對單程橫向流動換熱器的階躍響應(yīng)（英文）

1、Step Response of a Single-Pass Crossflow Heat Exchanger With Variable Inlet Temperatures and Mass Flow RatesKarthik Silaipillayarputhur PT Indo Kordsa Tbk, Citeureup, Indonesia 16810Stephen A. Idem Tennessee Tech Univers

2、ity, Cookeville, TN 38574The step response of a single-pass crossflow heat exchanger with variable inlet temperatures and mass flow rates was determined. In every instance, the energy balance equations were solved using

3、an implicit central finite difference method. Numerical predictions were obtained for cases where both the minimum or maximum capacity rate fluids were subjected to step changes in inlet temperature, coupled with step ma

4、ss flow rate changes of the fluids. Likewise, performance calculations were conducted for heat exchangers operating initially at steady state, where step flow rate changes of the minimum and maximum capacity rate fluids

5、were imposed in the absence of any temperature perturba- tions. Because of the storage of energy in the heat exchanger wall, and finite propagation times associated with the inlet pertur- bations, the outlet temperatures

6、 of both fluids do not respond instantaneously. A parametric study was conducted by varying the dimensionless parameters governing the transient response of the heat exchanger over a representative range of values. [DOI:

7、 10.1115/1.4007206]IntroductionThe design of a heat exchanger presumes accurate knowledge of fluid inlet temperatures and flow rates. However, in many instances, a heat exchanger does not operate at the design point. Und

8、er those circumstances, it is necessary to predict heat exchanger performance at off-design conditions. Heat exchangers do not instantaneously respond to changes in the inlet fluid temperatures and mass flow rates, and a

9、 finite time is required for the heat exchanger to stabilize from such variations. Perturbations in inlet fluid temperatures and flow rates will cause disturbances in the response of the heat exchanger, and these may int

10、roduce undesirable consequences to the process system. This paper addresses the development of a transient finite difference sensible performance model for a single-pass cross- flow heat exchanger. Variations of the inle

11、t fluid temperatures and mass flow rates as a function of time are considered. The paper details the pertinent governing equations and presents the results for various cases. Furthermore, to validate the transient perfor

12、mance model, the results obtained from the transient performance model for large times (where a steady solution is expected) are compared with predictions from a steady performance model. There are a great number of refe

13、rences available in the litera- ture pertaining to transient heat exchanger performance modeling. Only the most pertinent references are discussed herein. Spiga and Spiga [1] studied the two-dimensional transient behavio

14、r of gas- to-gas crossflow heat exchangers by solving the thermal balance equation by analytical methods. Spiga and Spiga [2] provided nondimensional solutions for transient temperature analysis of direct transfer crossf

15、low heat exchangers. Spiga and Spiga [3] studied the step response of a single-pass crossflow heatexchanger with finite wall capacitance. Mishra et al. [4] numeri- cally investigated the transient behavior of crossflow h

16、eat exchangers with longitudinal conduction and axial dispersion for step, ramp, and exponential hot fluid inlet temperature perturba- tions. Mishra et al. [5] developed a numerical scheme for studying the transient beha

17、vior of crossflow heat exchangers having finite wall capacitance for perturbations in both temperature and flow. The explicit finite difference approach was used, and the results were presented for step, ramp, exponentia

18、l, and sinusoidal varia- tion in the hot fluid inlet temperature. Dwivedi and Das [6] pre- sented a transient model to analyze the transient response of plate heat exchangers subjected to a step flow variation. Mishra et

19、 al. [7] analyzed the effects of temperature and flow nonuniformities on the transient response of crossflow heat exchangers.Transient Performance ModelThe current study directly follows from the work presented in Ref. [

20、5]. Figure 1 depicts a schematic representation of the single- pass crossflow heat exchanger considered in this study. Fluid ‘a(chǎn)’ and fluid ‘b’ exchange heat through a separating solid wall, and the flow direction of both

21、 fluids is normal to one another. In gen- eral, the designation of the ‘a(chǎn)’ fluid or ‘b’ fluid is completely arbi- trary. However, in this paper, it is convenient to define the ‘a(chǎn)’ fluid such that it has a capacity rate l

22、ess than or equal to that of the ‘b’ fluid. It is proposed that either fluid can experience a change in inlet temperature and/or mass flow rate. In order to con- sider a manageable number of cases, the present paper is r

23、estricted to situations where one fluid undergoes changes in inlet fluid con- ditions while the inlet conditions of the other fluid are presumed to remain constant in time. That constraint need not be imposed, and Ref. [

24、8] considers a number of other instances where transient inlet conditions of both fluids vary simultaneously. Additional assumptions made in this study, consistent with those outlined in Ref. [5], are as follows: (i) the

25、 thermophysical properties of both the fluids and walls are constant and uniform, (ii) both fluids are unmixed in the given pass, (iii) there is no phase change in the flu- ids, (iv) there is no internal heat generation

26、in either fluid, (v) the heat exchanger does not exchange heat with the surroundings, (vi) the temperature of both fluids does not vary in a direction normal to the separating solid wall, indicating that the fluid and wa

27、ll tem- perature variations are two-dimensional, (vii) the film heat trans- fer coefficient is solely a function of fluid velocity and changes with time as the flow rate simultaneously changes, and (viii) the effects of

28、fouling resistances are negligible. The capacity rate ratio can be expressed asCr ¼ ð _ mcÞa ð _ mcÞb ¼ 1E (1)The heat transfer resistance ratio is defined in terms of the convec- tion heat

29、transfer environments on either side of the exchanger wall, such thatR ¼ ðhAÞb ðhAÞa(2)Per Ref. [5], the flow perturbation can be expressed by defining the ratio of mass flow rate at any time t t

30、o that at initial time level such thatca ¼ _ m0 a _ ma ; cb ¼ _ m0 b _ m0 b(3)Assuming fully developed turbulent flow, the heat transfer coeffi- cient is proportional to mass flow rate. Therefore, the heat tran

31、sfer coefficient at any time t is defined as [5]h0 a ¼ cb aha (4) Manuscript received December 15, 2011; final manuscript received June 14, 2012; published online October 12, 2012. Assoc. Editor: Arun Muley.Journal

32、of Thermal Science and Engineering Applications DECEMBER 2012, Vol. 4 / 044501-1 Copyright V C 2012 by ASMEDownloaded From: http://thermalscienceapplication.asmedigitalcollection.asme.org/ on 03/11/2013 Terms of Use: htt

33、p://asme.org/termsobjective of the steady performance model is to serve as an input for those cases considered in this study where the heat exchanger experiences changes in the inlet fluid mass flow rates, in the ab- sen

34、ce of temperature inlet variations. Referring to Ref. [8], if the ‘a(chǎn)’ fluid is treated as the minimum capacity rate fluid after a mass flow rate change has occurred, the steady state temperatures of the fluids and the so

35、lid heat exchanger wall at successive grid loca- tions are determined by employing the following finite difference equations; refer to Fig. 1:Ta i þ 1; j ð Þ ¼ 1 ? a 1 ? Cr ð Þ1 þ a 1 &

36、#254; Cr ð Þ Ta i; j ð Þ þ 2a1 þ a 1 þ Cr ð Þ Tb i; j ð Þ(23)Tb i; j þ 1 ð Þ ¼ 1 þ a 1 ? Cr ð Þ1 þ a 1 þ Cr ð Þ

37、; Tb i; j ð Þ þ 2aCr 1 þ a 1 þ Cr ð Þ Ta i; j ð Þ(24)Tw i; j ð Þ ¼ cb a ðcb a þ Rcb bÞ Ta i; j ð Þ þ Rcb b ðcb a þ Rcb b

38、Þ Tb i; j ð Þ (25)wherea ¼ NTU2N (26)Likewise, if the ‘a(chǎn)’ fluid is treated as the maximum capacity rate fluid after the flow rate disturbance, the steady state temperatures of the fluids at successive

39、 grid locations are determined by using the following expressions [8]:Ta i þ 1; j ð Þ ¼ 2aCr 1 þ a 1 þ Cr ð Þ Tb i; j ð Þ þ 1 þ a 1 ? Cr ð Þ1 þ a

40、 1 þ Cr ð Þ Ta i; j ð Þ(27)Tb i; j þ 1 ð Þ ¼ 1 ? a 1 ? Cr ð Þ1 þ a 1 þ Cr ð Þ Tb i; j ð Þ þ 2a1 þ a 1 þ Cr ð Þ

41、Cr Ta i; j ð Þ(28)In this instance, the steady state wall temperature at any grid loca- tion is again given by Eq. (25). Equations (23)–(28) are solved subject to the same boundary conditions that were employed

42、 in the transient analysis. The above equations are employed to calcu- late the fluid ‘a(chǎn)’ and the fluid ‘b’ steady state temperature at suc- cessive grid locations. The outlet temperatures are therein averaged to yield t

43、he steady heat exchanger performance.ResultsBased on the concepts and the equations described in the ‘Transient Performance Model’ and ‘Steady Performance Model’ sections, a model is developed to study and validate the t

44、ransient finite difference sensible single-pass heat exchanger performance. The transient performance of the heat exchanger is studied over a range of parameters, and the steady state results obtained from the transient

45、performance model are compared with the results from the steady performance model in the limit as t ! 1. The salient observations pertaining to each case are discussed below. Figure 2 depicts the mean fluid exit temperat

46、ures from the tran- sient performance model plotted as a function of dimensionless time due to a step temperature change of the ‘a(chǎn)’ fluid inlet temper- ature at different overall number of transfer units (NTU) values, wh

47、ere E ¼ R ¼ 1, V ¼ 0, ca ¼ cb ¼ 1. In this case, it is assumed that both the fluids have a steady mass flow rate. The results from the transient performance model are compared with the analytical

48、 results presented in Ref. [1]. The fluid temperatures from Ref. [1] are presented as discrete points and the temperatures determined by the transient finite difference model are shown as solid lines. Figure 2 depicts ex

49、cellent agreement between the results obtained from the current finite difference approach and the results obtained through analytical approach [1], thus promoting confi- dence in the transient finite difference performa

50、nce model. Figures 3 and 4 depict the mean fluid exit temperatures calcu- lated from the transient performance model plotted as a functionFig. 3 Mean fluid exit temperature of the ‘a(chǎn)’ fluid due to a step change of the ‘a(chǎn)

51、’ fluid inlet temperature coupled with a step flow rate change of the ‘a(chǎn)’ fluid; initially E ¼ R ¼V ¼ NTU ¼ 1; cb ¼ 1Fig. 4 Mean fluid exit temperature of the ‘b’ fluid due to a step change of th

52、e ‘a(chǎn)’ fluid inlet temperature coupled with a step flow rate change of the ‘a(chǎn)’ fluid; initially E ¼ R ¼V ¼ NTU ¼ 1 and cb ¼ 1Fig. 2 Mean fluid exit temperature of the ‘a(chǎn)’ and ‘b’ fluids due to a s

53、tep temperature change of the ‘a(chǎn)’ fluid inlet temperature; E = R = 1, V = 0, ca = cb = 1Journal of Thermal Science and Engineering Applications DECEMBER 2012, Vol. 4 / 044501-3Downloaded From: http://thermalscienceapplic